On the Asymptotic Properties of LDU-Based Tests of the Rank of a Matrix
指出Gill和Lewbel基于LDU分解的矩阵秩检验的渐近分布仅在极有限情形下正确，一般情形下为复杂非线性函数，但LDU分解可用于构造与最小X²检验渐近等价的检验。
Abstract Gill and Lewbel recently introduced a test for the rank of a matrix based on the LDU decomposition. Unfortunately, the asymptotic distribution suggested by them is incorrect except in a very limited problem. In general, the asymptotic distribution is that of a highly complicated nonlinear function of a normally distributed random vector that appears to defy useful characterization. The LDU decomposition can be used to produce a valid test asymptotically equivalent to the minimum-X 2 test.